In general one frequently takes \({\phi _1}={\phi _2}\) , but it is also possible to consider penalties \({\phi _1}(\pi _1|)\)  and \({\phi _2}(\pi _2|)\)  with \(\phi _1\ne \phi _2\) .
For instance, take \({\phi _1}=\iota _{(=)}\)  and \({\phi _2}=\rho \)  (as in [1]}), or \({\phi _i}=\rho _i\)  with \(\rho _1\ne \rho _2\)  (as in [2]}).
It is relevant in domain adaptation where \(\)  is a source dataset on which a predictor was trained, and \(\)  is a similar but shifted dataset on which we want to transfer the learned predictor [3]}.
